Abstract:
The National Curriculum Statement (NCS), implemented in 2003, marked the formal introduction of mathematical modelling into the South African curriculum. This represented a significant shift, as mathematical modelling had previously been largely absent from the curriculum. This study investigated the mathematical modelling proficiency of Grade 11 learners from three high schools in the Pongola Circuit, KwaZulu-Natal Province, with a specific focus on determining their competency in solving non-routine problems.
The study was motivated by the observation that many teachers did not receive adequate training in mathematical modelling during their pre-service education. Existing research indicates that inadequately trained teachers can negatively affect learners’ academic performance. Furthermore, the teacher is widely regarded as the most critical agent in the successful implementation of instructional reforms at the classroom level (Shepherd, 2019; Theophile et al., 2020). It was therefore necessary to examine learners’ competencies in mathematical modelling.
Learners’ competencies were assessed using the five-step modelling process proposed by Kaiser and Stender (2013), which includes: (1) understanding the problem, (2) formulating a mathematical model, (3) solving the model, (4) interpreting the results, and (5) validating the results. For a learner to be considered competent in mathematical modelling, all five stages of the process had to be correctly executed.
A total of 75 Grade 11 learners from three purposively selected schools participated in the study. Qualitative data were collected through document analysis. The data analysis process involved familiarisation with learners’ written responses, followed by thematic analysis to interpret meaning, identify patterns, and generate insights related to the research questions.
The findings revealed that all learners demonstrated incomplete competency in mathematical modelling. Specifically:
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None of the learners successfully completed all five stages of the modelling process in any of the four test questions.
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Learners did not make or attempt to make assumptions, which are essential in solving real-life problems.
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Variables were used without clear definitions, and final solutions were often expressed in terms of unidentified variables. This indicated a lack of interpretation of results within the context of the real-world problems. Interpretation involves translating mathematical outcomes back into meaningful real-life conclusions.
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Learners did not verify or validate their solutions. Validation is critical for assessing the accuracy and appropriateness of both the mathematical model and its results in relation to the real-world context.
The findings suggest that Mathematics teachers should be encouraged to adopt a mathematical modelling approach in teaching and learning. It can be inferred that learners had limited or no exposure to mathematical modelling, as key processes—such as defining variables, making assumptions, interpreting results, and validating solutions—were consistently omitted. According to the Curriculum and Assessment Policy Statement (CAPS), mathematical modelling should serve as a central focus of the Mathematics curriculum (Department of Basic Education [DBE], 2011). Therefore, the Department of Education has a responsibility to ensure the effective implementation of mathematical modelling, emphasising the integration of real-life contexts across all aspects of the curriculum.
